Question

You invest $10,000 in 20-year zero coupon bonds, and another $10,000 in 30-year zeros. What are the duration and convexity of the portfolio?

Answer 1

In a zero coupon bond on payment is payment of Face value of the bond at the maturity of it. So the Duration of a zero coupon bond is same as its maturity.

For a 20-year zero coupon bonds, duration = 20 years

Weight of this bond = 10000/(10000+10000) = 0.50

For a 30-year zero coupon bonds, duration = 30 years

Weight of this bond = 10000/(10000+10000) = 0.50

So duration of the portfolio = weight average duration of these two bond = 0.5*20 + 0.5*30 = 25 years.

Convexity of a zero coupon bond maturing at time T is given by T^2

So, for a 20-year zero coupon bonds, convexity = 20^2 = 400

For a 30-year zero coupon bonds, convexity = 30^2 = 900

So convexity of the portfolio = weighted average convexity of these two bond = 0.5*400 + 0.5*900 = 650